What does a=? b=? Angle B=?

a) The variables are the variable unit cost of candles and the fixed cost of shipping.

b) The information given in the question include the total costs for 4 candles and 12 candles, including their shipping costs.

c) An equation representing the situation is given as

d) Allie can get 18 candles for $60.

An equation is a mathematical statement showing that two or more algebraic expressions are equal or equivalent.

Algebraic expressions combine variables, values, constants, and numbers without the equal symbol (=), but they use the mathematical operands.

The total cost for ordering 4 candles = $35

The total cost for ordering 12 candles = $49

The difference = 8 candles = $14

Unit cost of candles = $1.75 ($14 ÷ 8)

Shipping (fixed) cost for the first order = $28 ($35 - $1.75 x 4)

Shipping (fixed) cost for the second order = $28 ($49 - $1.75 x 12)

For ordering candles for $60, the number of candles Allie can get = 18 ($60 - $28) ÷ $1.75

Learn more about equations at https://brainly.com/question/2972832.

#SPJ1

Answer:

x - 1

Step-by-step explanation:

1st number = x - 1

middle number = x

3rd number = x + 1

Answer:

-4.21 ft. below sea level

Step-by-step explanation:

The expression is -45.32 + 41.11, and so you are basically just doing 45.32-41.11, but the answer will be negative.

45.32-41.11=4.21, but the answer is negative, so -4.21.

Answer:

b

Step-by-step explanation:

3x≥-6

x≤-2

Answer:

a

Step-by-step explanation:

Solving the inequality

3x - 5 ≥ - 11 ( add 5 to both sides )

3x ≥ - 6 ( divide both sides by 3 )

x ≥ - 2

Since x is greater than or equal to - 2, then this is indicated on the number line by a closed circle at - 2

Since x greater than - 2 then the arrow points to the right

This is represented in graph a

Answer:

The equation that relates distance, rate, and time is

       d  =  rt

Step-by-step explanation:

The measure of angle x is 140°

For given question,

We are given that a pair of parallel lines is cut by a transversal line .

Let a pair of parallel lines are PQ and RS and the transversal line AB cut the parallel lines PQ and RS.

We are given that an exterior angle on the left side of the transversal line is 40 degrees.

The interior angle on the right side of transversal line is x which is not vertical opposite to exterior angle = 40 degrees

We know that when two lines are parallel and cut by a transversal line then corresponding angles are congruent.

So, angle MNR = 40°

Also, ∠MNR + ∠MNS = 180°           ...............(linear pair of angles)

⇒ 40° + x = 180°

⇒ x = 140°

Therefore, the measure of angle x is 140°

Learn more about the angles formed by parallel lines and transversal here:

https://brainly.com/question/12851990

#SPJ4

The leading coefficient of the polynomial is -2, and the degree of the polynomial is 3.

To identify the leading coefficient and degree of the polynomial, we need to consider the highest power of the variable in the polynomial expression.

In the given polynomial, -2y³ is the term with the highest power of y. The coefficient of this term, which is -2, is the leading coefficient of the polynomial. The degree of a polynomial is determined by the highest power of the variable. In this case, the highest power of y is 3 in the term -2y³. Therefore, the degree of the polynomial is 3.

LEARN MORE ABOUT coefficient here: brainly.com/question/13431100

#SPJ11

Answer:

45/4

Step-by-step explanation:

Answer: XY= 11.25

Step-by-step explanation:

So if the shapes are similar than the dimensions are similar also. So check it right we know that 12 doesn't go into 27 but we can still divide to solve for the dimension. so 27/12 = 2.25. We can also check this answer by multiplying 8 by 2.25 to hopefully get 18 since side AC is similar to side XZ. Since our numbers check out we can mulitply 5*2.25 to get 11.25 as the side for XY

Answer:5/6

Step-by-step explanation:

simplify

The median of the test marks is 28.5.

The median is the value in the middle of a data set, meaning that 50% of data points have a value smaller or equal to the median and 50% of data points have a value higher or equal to the median. For a small data set, you first count the number of data points (n) and arrange the data points in increasing order.

Marks obtained for the test 49 34 20 15 18 38 29 28 25 30.

15, 18, 20, 25, 28, 29, 30, 34, 38, 49

The highest mark scored by a learner is 49

The median of the test marks is (28+29)/2

= 28.5

Therefore, the median of the test marks is 28.5.

Learn more about the median here:

https://brainly.com/question/28060453.

#SPJ1

Answer:

\( \longmapsto(x - 1)(2x + 3) \\ = 2 {x}^{2} + 3x - 2x - 3 \\ = \boxed{2 {x}^{2} + x - 3}\)

Answer:

B

Step-by-step explanation:

multiply 10000 by .05 = 500

multiply the remaining 2350 by .03 = 69

Add 500+69= 569

Answer:

Use a punnet square type of diagram

Step-by-step explanation:

The x-intercept of the line calculator is (-1,0) while the y-intercept is (0,-3).

To determine the x-intercept, let y = 0 and solve for x in the equation y = 3x - 1.

Substitute 0 for y in the equation.0 = 3x - 1

Add 1 to both sides1 = 3x

Divide both sides by 3x = 1/3

The x-intercept of the line is (1/3, 0).

To find the y-intercept, let x = 0 and solve for y in the equation y = 3x - 1.

Substitute 0 for x in the equation.y = 3(0) - 1y = -1

The y-intercept of the line is (0, -1).

Therefore, the x-intercept is (1/3, 0), and the y-intercept is (0, -1).

Therefore, The x-intercept of the line calculator is (-1,0) while the y-intercept is (0,-3). The calculation above supports the conclusion.

To know more about, line calculator, visit

https://brainly.com/question/30763905

#SPJ11

Given that the closed rectangular box has a square base and a capacity of 27 in³ and it is constructed with the least

amount of material. Now, we have to find the dimensions of the box.To find the dimensions of the box we need to use the following formula:V = lwh ...(1)whereV = volume of the rectangular boxl = length of the boxw = width of the boxh = height of the boxGiven that, V = 27 in³ and the base of the box is a square. That is, l = wUsing this in equation (1), we get27 = l²h27 = w²hNow we need to minimize the surface area.

The surface area can be given by the formula:S.A. = 2lw + 2lh + 2whwhere S.A. = Surface Area of the box.Now substituting l = w in equation (1),

we get27 = l²h27 = w²h

Then, h = 27 / l² ...(2)Substituting equations (1) and (2) in surface area, we get:S.A. = 2lw + 2lh + 2wh= 2lw + 2l(27 / l²) + 2w (27 / l²)= 2l²w⁻¹ + 54l⁻¹ + 54w⁻¹Now we need to minimize S.A. with respect to l. That is we need to find dS.A./dlS.A. = 2l²w⁻¹ + 54l⁻¹ + 54w⁻¹Differentiating w.r.t l,dS.A./dl = 4lw⁻¹ - 54l⁻²Now to find the minimum value, we have to equate the derivative to zero.(dS.A./dl) = 4lw⁻¹ - 54l⁻² = 0or4 / l = 54 / w²Multiplying both sides with l² / 4, we getl² / 4 = 54 / w²l = 6w / √3Putting this value of l in equation (1), we get:27 = l²h27 = (6w / √3)²h27 = 12w²h/3h = 9 / w²Now, we need to minimize S.A. with respect to w. That is we need to find dS.A./dwS.A. = 2lw + 2lh + 2wh= 2lw + 2l(9 / w²) + 2ww⁻¹= 2lw + 18w⁻¹ + 2wNow differentiating w.r.t w,dS.A./dw = 2l w⁻¹ - 18w⁻² + 2Differentiating w.r.t w again to find whether it is maximum or minimum, we get:d²S.A./dw² = -2lw⁻² + 36w⁻³The value of d²S.A./dw² is negative. Hence the given equation has a maximum.So, to minimize the surface area, the value of l and w should be equal.

So, l = w = 3√3.Then h = 9 / (3√3)² = 1√3∴ The dimensions of the box are 3√3 x 3√3 x 1√3 cubic inches.

To know more about pentagon visit:

https://brainly.com/question/17054992

#SPJ11

Step-by-step explanation:

f(x) - g(x)

9x³+2x²-5x+4 - (5x³-7x+4)

9x³+2x²-5x+4 - 5x³+7x-4

4x³+2x²+2x

2x(2x²+x+1)

Answer:

15 Apr 2018 — Area of path parallel to the remaining length of ... Area of parallelogram ABCD = AB × AE = 8 × 4 cm2 ... We can also calculate area of shaded portion by using area of..

Answer:

185.25 cm^2

Step-by-step explanation:

since only length is given i considered the wall as square shape. So given :

length = 13.5 cm

area of the wall = l^2

= 13.5^2

=182.25 cm^2

Answer:

9/10 < 7/5

Step-by-step explanation:

7/5 = 14/10

9/10 < 14/10

Answer:

7/5 is greater than 9/10

Step-by-step explanation:

7/5 = 14/10

The correct option is B. The complete collection of all elements, individuals, measurements, scores, or other entities that are of interest and relevant to a particular study or analysis is called the population.

A collection is a group of items that have been gathered or accumulated together based on a particular theme or purpose. Collections can be made up of physical objects such as books, stamps, coins, or artwork, as well as digital items like photos, music, or videos. Collections can also refer to data structures in computer programming that hold groups of related items.

People often collect items as a hobby or passion, and the act of collecting can bring a sense of fulfillment, enjoyment, and satisfaction. Collections can have both sentimental and monetary value, and they may be displayed in personal or public settings, such as museums or galleries. The process of collecting often involves researching and acquiring new items, as well as organizing and preserving the existing collection.

To learn more about Collection visit here:

brainly.com/question/5775675

#SPJ4

#a

Degree is the highest power

#b

Leading coefficient is 7

#c

Constant term is 8 (which doesn't contain variables)

#d

Leading term is term with highest power

The problem can be solved using the simplex method, and the solution can be verified using the graphical method. The optimal solution is X1 = 6, X2 = 0, X3 = 6, Z = 24.

The problem can be solved using the simplex method, and verified using the graphical method. Here are the steps:

Convert the problem to standard form by introducing slack variables:
Min Z = -2X1 - 4X2 - 3X3 + 0S1 + 0S2 + 0S3
St. X1 + 3X2 + 2X3 + S1 = 30
X1 + X2 + X3 + S2 = 24
3X1 + 5X2 + 3X3 + S3 = 60
Xi, Si >= 0

Set up the initial simplex tableau:
| 1 3 2 1 0 0 30 |
| 1 1 1 0 1 0 24 |
| 3 5 3 0 0 1 60 |
| 2 4 3 0 0 0 0 |

Identify the entering variable (most negative coefficient in the objective row): X2

Identify the leaving variable (smallest ratio of RHS to coefficient of entering variable): S1

Pivot around the intersection of the entering and leaving variables to create a new tableau:
| 0 2 1 1 -1 0 6 |
| 1 0 0 -1 2 0 18 |
| 0 0 0 5 -5 1 30 |
| 2 0 1 -2 4 0 36 |

Repeat steps 3-5 until there are no more negative coefficients in the objective row. The final tableau is:
| 0 0 0 7/5 -3/5 0 18 |
| 1 0 0 -1/5 2/5 0 6 |
| 0 0 1 1/5 -1/5 0 6 |
| 0 0 0 -2 4 0 24 |

The optimal solution is X1 = 6, X2 = 0, X3 = 6, Z = 24.

To verify the solution using the graphical method, plot the constraints on a graph and find the feasible region. The optimal solution will be at one of the corner points of the feasible region. By checking the values of the objective function at each corner point, we can verify that the optimal solution found using the simplex method is correct.

In conclusion, the problem can be solved using the simplex method, and the solution can be verified using the graphical method. The optimal solution is X1 = 6, X2 = 0, X3 = 6, Z = 24.

Learn more about Graphical method

brainly.com/question/29193266

#SPJ11

The slope-intercept form of the equation is y = - mx + b.

The equation of a line can be expressed in a variety of ways. Although they may differ in appearance, all of them describe the same line because multiple equations can describe the same line. However, all linear equations describing the same line are equivalent.

The formula y = mx + b can be used to represent any straight line. Any straight line equation, known as a linear equation, can be expressed as y = mx + b, where m denotes the line's slope and b its y-intercept. The value of y at the line's intersection with the y-axis is its y-intercept.

Given a graph of the equation, choose two points on the line and use them to calculate the slope in order to put the equation in slope-intercept form. This is the answer to the equation's question. Next, determine the y-coordinates, intercept's which should be of the type (0,b). The value in the equation is the y-coordinate.

Thus, the equation derived from the graph is as follows:

Since we are aware that the slope here is negative,

Therefore Our formula is y = -mx + b.

To learn more about Linear Equations, visit: https://brainly.com/question/29739212

#SPJ4

Answer:

115 apples were picked last year

Step-by-step explanation

It says there are 50% more apples picked this year than last year. So, we divide 230 by 2 because 50% is half of 100%. 230÷2 = 115

115 apples

Answer:

x=10

Step-by-step explanation:

3(4x-12) = 84

Divide each side by 3

3/3(4x-12) = 84/3

4x-12 =28

Add 12 to each side

4x-12+12 = 28+12

4x= 40

Divide each side by 4

4x/4 = 40/4

x = 10

Answer:

what gas station I presume is the answer

The counterexample to the conjecture "if x < 3, then x² < 9" is x = - 4, as it satisfies the condition x < 3 but does not satisfy the result x² < 9.

The counterexample to the given conjecture "if x < 3, then x² < 9" would be a value of x that is less than 3 but whose square is not less than 9. Let's find such a counterexample:

If we take x = - 4, we can see that x is less than 3, as required by the conjecture. However, when we square x, we get x² = 16, which is not less than 9. Therefore, x = - 4 serves as a counterexample to the conjecture.

In summary, the counterexample to the conjecture "if x < 3, then x² < 9" is x = - 4, as it satisfies the condition x < 3 but does not satisfy the result x² < 9.

Learn more about Conjecture here

https://brainly.com/question/29367550

#SPJ4

In the given relations , the relation (B) represents a function, others are not function. To become a function each input should have only one output. Since others does not satisfy this criteria they are not functions.

To learn more about relations refer to :

https://brainly.com/question/24779057

#SPJ13

we can express the x coordinate as tsin(t) and the z coordinate as tcos(t). This gives us the vector parametrization of the curve: x = tsin(t), z = tcos(t).

we can express the x coordinate as tsin(t) and the z coordinate as tcos(t). This gives us the vector parametrization of the curve: x = tsin(t), z = tcos(t).

The xz-plane is the plane formed by the x-axis and the z-axis. To find a vector parametrization of a curve in this plane, we need to express the x and z coordinates of the curve as functions of a parameter t. In this case, we can express the x coordinate as tsin(t) and the z coordinate as tcos(t). This gives us the vector parametrization of the curve: x = tsin(t), z = tcos(t).

learn more about coordinate here

https://brainly.com/question/27749090

#SPJ4

The average mass of a person is 73 kg, and the distance their center of mass rises after leaving the ground is approximately m/s.

To calculate the distance the average person's center of mass rises after leaving the ground, we can consider the concept of work-energy theorem. When a person jumps, the work done on their body is equal to the change in their kinetic energy. Assuming there is no external work done on the person, the initial kinetic energy is zero. Therefore, the work done on the person is equal to the final kinetic energy.

The work done on an object is given by the equation W = Fd, where W is the work, F is the force, and d is the displacement. In this case, the force acting on the person is their weight, which can be calculated using the formula F = mg, where m is the mass and g is the acceleration due to gravity (approximately 9.8 m/s²). The displacement is the distance the center of mass rises, which is what we need to find.

The work done on the person can be expressed as W = mgh, where h is the height or distance the center of mass rises. Equating this to the final kinetic energy, we have mgh = (1/2)mv², where v is the velocity of the person when leaving the ground. Since the initial kinetic energy is zero, we can simplify this equation to mgh = (1/2)mv².

We can rearrange this equation to solve for h: h = (1/2)v²/g. Plugging in the values, with the mass m = 73 kg and g = 9.8 m/s², we can calculate the value of h. However, the velocity v is not provided, so we cannot determine the exact value of h.

Learn more about height here:

https://brainly.com/question/29131380

#SPJ11